Machine learning / artificial intelligence accelerates the progress in all research fields, fuels the fourth industrial revolution and transforms our daily lifes. Increasing computer power, rapidly improving methods of machine learning and the availability of ever increasing amounts of high quality data facilitate a paradigm shift from first-principle based deductions to data-driven discoveries and modeling. Fluid mechanics, historically a field of big data, is no exception. In addition, machine learning provides increasingly powerful methods for the challenging optimization problems faced in aerodynamic engineering. This course will outline established state-of-the-art methods of machine learning and demonstrate their application in high-challenge applications of fluid mechanics, like analyses, discovery of equations, dynamic modeling, control, turbulence closures and shape optimization. This course is aimed at Ph.D. students and Master students in all fields of fluid mechanics. Researchers interested in the potential of machine learning are also welcome to attend this course.

The literature of fluid mechanics contains myriad of machine learning applications. The curriculum aims to pair methods with problems, i.e. present machine learning methods in a natural application environment. Thus the power of each method can immediately be assessed. The applications belong to 6 fields.
1. Analysis of coherent structures. Low-dimensional flow representations have been at the core of theoretical fluid dynamics, starting with vortex models in the 1870s. Machine learning allows to distill low-dimensional Galerkin expansions and nonlinear manifolds from data. A low-dimensional state space is a critical enabler for understanding, full-state estimation, prediction and optimization.
2. Nonlinear dynamics. Hitherto, new equations have typically been derived from first principles. Machine learning enables to distill predictive human interpretable ordinary/partial differential equations from data.
3. Sparse data/rare events. Most engineering problems, e.g. for many involved parameters or for rare events, will never have enough data for a purely empirical characterization. A probabilistic framework is presented to compensate for lack of data.
4. Turbulence closures. Practically every engineering simulation is based on eddy viscosity, wall models and related closure simplifications. Machine learning harnesses rich data sets to develop more accurate closures.
5. Turbulence control. Modern computer and hardware developments provide an eldorado of unprecedented control opportunities with dramatic aerodynamic performance improvements, e.g. powerful actuators and sensors and smart skins. Machine learning facilitates an automated learning of nonlinear control laws.
6. Shape optimization. Over hundred years, the shape of every high-speed transport vehicle and flow machine has been systematically improved for aerodynamic performance based on first principles and experience. Machine learning offers new automated approaches for these high-dimensional optimization problems.

This course aims to synergize machine learning methods with first principle knowledge of fluid mechanics.